(Of course, given a finite sample of draws from \({\cal D}\) , this is typically done by minimizing the corresponding expectation over the sample.) It is well known that if \({\cal D}\)  is linearly separable with margin \(\gamma >0\) , then for
a range of different choices of the convex potential function \(\phi \)  (including the AdaBoost, MadaBoost and LogitBoost potential functions described above),
greedy iterative algorithms that perform coordinatewise gradient descent to minimize \(P_{\phi ,{\cal D}}\) 
will drive the misclassification error
\(\Pr _{(,) \sim {\cal D}}[\ne (v \cdot )]\) 
to zero.
Indeed, the AdaBoost [1]}, MadaBoost [2]} and LogitBoost [3]}
boosting algorithms correspond precisely to greedy coordinatewise gradient descent procedures of this sort; see [4]} for details.
